Both Canon S110 and Fujifilm X20 have 12.0 MP resolution sensors but Canon S110's sensor is 1/1.7-inch (7.44 x 5.58 mm ) and Fujifilm X20's sensor is 2/3-inch (8.8 x 6.6 mm ).
Since Fujifilm X20's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Canon S110.
Below you can see the S110 and X20 sensor size comparison.
Sensor Size and Resolution Comparison image of Canon S110 and Fujifilm X20 Cameras
As seen above, Fujifilm X20 has a 1.4x Larger sensor area than Canon S110. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Canon S110
or the
Fujifilm X20 ,
including hyperfocal distance.
One thing to watch when comparing these two: they have different sensor sizes
(1/1.7-inch versus 2/3-inch),
so compare them at the same framing rather than the same focal length.
Put the same focal length on the smaller sensor and it will show less depth of
field, not more, because it also crops tighter. The calculator shows the
full frame equivalent focal length for each body so you can match the framing.